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Capillary tubes are widely used as expansion device in small scale refrigeration systems.
isobutane
ielle
Although capillary tubes have been used as expansion device
of the vapor refrigeration cycle especially in small scale sys-
tems like household refrigerators or small air conditioning
systems formany decades, to design a capillary tube for a given
refrigeration cycle is still amost empirical and time consuming
enomena inside the
us pressure drop and
evaporation of the refrigerant, an analytic and explicit
description of the total throttling process is not possible.
Therefore many attempts have been done to develop simple
design methods in the past. These design methods always
imply certain simplifications or assumptions and must be
* Corresponding author. Tel.: 49 721 608 42730.
Available online at www.sciencedirect.com
e:
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0E-mail address: schenk@kit.edu (M. Schenk).Mots cles : Tube capillaire adiabatique ; R600a ; Resultats experimentaux ; Ecoulement amorti ; conception factor
1. Introduction process. Due to the complex flow phcapillary tube, caused by the simultaneoEtude experimentale de lecoulement du frigorige`ne(R600a) dans des tubes capillaires adiabatiquesArticle history:
Received 27 June 2013
Received in revised form
29 August 2013
Accepted 31 August 2013
Available online 9 September 2013
Keywords:
Adiabatic capillary tube
R600a
Experimental results
Factorial design
Choked flow0140-7007/$ e see front matter 2013 Elsevhttp://dx.doi.org/10.1016/j.ijrefrig.2013.08.024Despite the simple geometry one finds complex physical processes during the throttling in
the capillary tube, which were subject of many studies in the last decades. However, there
is currently only one source of experimental data for the refrigerant isobutane (R600a) and
adiabatic capillary tubes (Melo et al., 1999). In order to close this gap a test rig was built and
experimental data in the range of typical small scale refrigeration systems was collected.
The measured mass flow rates span from 0.64 kg h1 to 1.93 kg h1. Additionally, the effect
of critical flows (Choked Flow) is shown by means of an extra performed test. The semi-
algebraic equation from Hermes et al. (2010) showed a remarkable level of agreement by
predicting 94% of all points within a 10% error band. 2013 Elsevier Ltd and IIR. All rights reserved.a r t i c l e i n f o a b s t r a c tof isobutane (R600a) through adiabatic capillarytubes
Matthias Schenk*, Lothar R. Oellrich
Karlsruhe Institute of Technology (KIT), Institute for Technical Thermodynamics and Refrigeration, Engler-Bunte-
Ring 21, 76131 Karlsruhe, GermanyExperimental investigation of
www. i ifi i r .org
journal homepagier Ltd and IIR. All rightse refrigerant flow
www.elsevier .com/locate/ i j refr igreserved.
validated with experimental data. The experiments must al-
ways be done in the same range as the design method is going
to be used. Especially in the case of Isobutane (R600a), which is
nowadays a commonly used refrigerant in small scale refrig-
eration systems, there is only one source of experimental data
available (Melo et al. (1999) and reviewed by Khan et al. (2009)).
Up tonowonly 19data pointshavebeenpublished,where in
all experiments the same inner diameter was used. The tests
were donewith high condensation pressures (7.1e11.3 bar) and
high mass flow rates were measured (2e4 kg h1). Both pa-rameters are much higher than the usual conditions in typical
small scale refrigeration systems. Thispaper aims to extend the
2. Experimental work
Nomenclature
D inner diameter (m)
L length of capillary tube (m)_M mass flow rate (kg s1)p pressure (Pa)
T temperature (C)DTsub subcooling degree (
C)v specific volume (m3 kg1)
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 02762.1. Experimental setup
Fig. 1 shows the scheme of the workbench which was built
and used to perform the presented tests. The workbenchavailable database for R600a and adiabatic capillary tubes to
lower mass flow rates and check the validity of existing design
methods proposed in the literature in this range. First results
were already published in (Schenk and Oellrich, 2012).Fig. 1 e Scheme of the workbench.basically represents a simple vapor-compression refrigeration
cycle. The compressor is a 9 cm3 hermetic variable velocity
compressor, whose frequency range spans from 20 to 75 Hz. In
order to avoid oil contamination in the test section, the
refrigerant passes through one oil separator and two oil filters
with 0.01 mm as smallest filtering element particle size. Both
oil separator and filters are supplied with electrical heaters
that are used to eliminate the risk of refrigerant condensation.
In order to control the high-side pressure, a proportional
valve is placed after the compressor. With the valve the mass
flow rate to the condenser can be regulated. The condenser is
a fan supplied tube-and-fin heat exchanger using an electrical
heater to set up the air temperature at the entrance. There-
fore, the capillary tube inlet pressure, i.e. the condensation
pressure, can be set through the valve opening, heater power
and fan frequency control.
After the condenser the liquid refrigerant flows through a
subcooler consisting of several Peltier elements attached to a
copper block embedding the refrigerant tube. The subcooled
liquid flows through a Coriolis mass flow meter. Next, a filter
dryer is used to hold back humidity or impurities that could
clog the capillary tube. The inlet temperature of the capillary
tube is controlled by an electrical preheater. In a sight glass
after the preheater and prior to the capillary tube inlet one can
check for the presence of bubbles in the refrigerant flow.
The inlet and outlet temperatures are measured with
mineral insulated K-type thermocouples, each 0.5 mm in
diameter, whose probes are positioned directly in the flow.
The inlet pressure is measured using a piezoresistive pressure
transducer. After the capillary tube the refrigerant enters the
tubular evaporator equipped with an electrical heater. The
power of the heater can be adjusted to ensure that only su-
perheated vapor exits the evaporator. Then the refrigerant
flows back to the compressor.
All pressure transmitters and thermocouples were cali-
brated before the measurements. The coriolis mass flow
Greek Letters
r density (kg m3)
F capillary constant (6.0)
Subscripts
in inlet to the capillary tube
out outlet of the capillary tube
f entrance in the two-phase domain
s saturation statemeter was calibrated by the manufacturer. The inner diam-
eter of the capillary tubes was determined by means of mi-
croscope pictures. Short pieces of the capillary were welded
into a copper block and afterward the surface of the block was
milled and polished. The flow area on the pictures was
marked and calculated with appropriate software. Doing this
at several points before and after the tested capillary tube, the
equivalent inner diameter was obtained. All the uncertainties
of the measurements are listed in Table 1.
The stated purity of the refrigerant by the manufacturer
was 98.5% isobutane. The refrigerant was filled into the cycle
from the liquid phase. Also the measured temperature in the
two-phase flow after the capillary tube corresponded with the
planning of the tests (Box et al., 2005). For all available test
this fact an extra test was performed where all parameters
2.4. Experimental results
In Table 4 the results of all test runs (Design of Experiments
and additional tests) are listed. The values of DTsub were
calculated with the equation for the vapor pressure given in
Bucker and Wagner (2006). In all tests the outlet pressure was
set below the critical pressure for the choked flow occurrence
(see Section 2.3) by adapting the compressor frequency. The
its implementation demand a high degree of time and effort.
Table 2 eMinimum and maximum values for the Designof Experiments.
Parameter () () Physical unitpin 4.5 6.0 bar (minuscules)
DTsub 8.0 13.0C
D 0.69 0.61 mm
L 2.5 3.9 m
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0 277were kept constant with the outlet pressure continuously
lowered during 4.5 h from 2.2 bar to 0.6 bar. Fig. 2 shows theparameters a minimum and maximum value were fixed: (1)
the inlet pressure pin, (2) the subcooling degree at the capillary
inlet DTsub, (3) the inner diameter D and (4) the length L of the
capillary tube. The chosen minimum and maximum values
are given in Table 2. These values are combined in a scheme in
away that all possible combinations are each reproducedwith
one run, which results in a total amount of 42 16 test runs.The scheme is shown in Table 3.
Because the individual test runs of this scheme combine
always the edges of the operating range (e.g. the highest
condensation pressure together with the biggest diameter),
very high subcooling degrees were chosen to avoid two phase
flow at the capillary tube entrance.
To broaden the scope of the presented data, also tests with
a lower subcooling at the capillary entrance and additional
three different capillary tubes (tests 17e22 in Table 4) were
performed.
2.3. Choked flow
As can be seen in Section 2.2 the outlet pressure was not
considered as a parameter in the design of experiments, due
to its marginal influence on the mass flow rate. To illustratecalculated saturation temperature of the measured pressure
and thus indicated a pure refrigerant.
2.2. Design of experiments
In order to cover the complete scope of conditions of small
scale refrigeration systems with a minimal amount of test
runs, the Two-level Factorial Design method was used for the
Table 1 e Uncertainties of the measurements.
Measured parameter Uncertainty
Temperature 0.2 CPressure 5 mbarMass flow rate 1%Inner diameter 0.01 mmCapillary tube length 5 mmresulting mass flow rate versus the outlet temperature of the
capillary tube.
The very small instabilities of the inlet pressure, which
resulted in a standard deviation over all points in these 4.5 h of
only 15 mbar, were noticeable on the enlarged scale of the
mass flow rate. In order to point out the effect of the inlet
pressure fluctuations, all data points for which the deviation
of the inlet pressure to itsmean valuewaswithin the standard
deviation are printed as filled circles. The other points are
presented as empty circles.
Fig. 2 clearly illustrates, that the mass flow rate does not
change anymore as the outlet pressure falls below 1.3 bar.
This is the range of Choked Flow.Additionally the discretisation of the process brings up
Table 3 e Scheme for the two-level factorial design (Boxet al., 2005).
Test pin DTsub D L
1 2 e Low Pressure Control Valve was kept fully open in all tests.
3. Comparison with available correlations
Due to the drastic change of the fluid properties in the two-
phase flow along the capillary tube, it is not possible to
describe the throttling process with analytical and explicit
equations. In order to obtain a reliable tool for the design of
capillary tubes in spite of these difficulties the following ap-
proaches evolved during the last decades:
3.1. Finite-volume based methods
Following the finite-volume based methods the capillary tube
is divided into single cells and the fluid properties are aver-
aged over these cells. Thus an accurate description of the
process is obtained. However, the creation of the model and3 e 4 e e 5 e 6 e e 7 e e 8 e e e 9 e10 e e11 e e12 e e e13 e e14 e e e15 e e e16 e e e e
Table 4 e Experimental results.
Test pin/bar Tin/C Tout/C L/m
Tests from the Design of Experiments e scheme
1 6.02 32.0 19.9 3.932 4.52 21.0 21.3 3.933 6.04 37.0 21.7 3.934 4.49 26.0 21.3 3.935 6.02 32.0 23.2 3.936 4.53 21.0 25.3 3.937 6.02 37.0 24.2 3.938 4.51 26.0 21.5 3.939 6.00 31.9 16.7 2.4910 4.50 21.0 19.5 2.4911 6.02 37.0 15.4 2.4912 4.48 26.0 20.3 2.4913 6.01 32.0 20.6 2.5314 4.50 21.0 25.9 2.5315 6.02 37.0 20.6 2.5316 4.50 26.1 24.7 2.53Additional tests
17 4.10 27.7 19.5 2.7318 5.30 34.1 21.9 2.7319 5.30 37.0 19.6 2.7920 4.00 23.7 11.2 2.7921 4.00 27.0 26.7 4.0422 5.29 34.0 25.9 4.04
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0278numerical issues one has to handle (Melo et al., 1992). Exam-
ples of this approach are given in Bansal and Rupasinghe(1998), Li et al. (1990) or Garca-Valladares et al. (2002).
Because of the named drawbacks this approach is not
further followed up in this work.
-30 -20 -10 0 101,20
1,22
1,24
1,26
1,28
1,30pin inside (5.0 +/- ) barpin outside (5.0 +/- ) bar
M/(
kgh-
1 )
Tout / C
0,5 1,0 1,5 2,0 2,5
pS(Tout) / bar
Tin = 27C =0.06 Kpin = 5.0 bar =0.015 bar
Choked Flow
Fig. 2 e Illustration of choked flow.3.2. Empirical correlations
D/mm DTsub/C pSTout/bar _M/(kg h1)
0.692 12.9 0.73 1.535
0.692 13.0 0.69 1.379
0.692 8.0 0.67 1.340
0.692 7.7 0.69 1.280
0.611 12.9 0.63 1.104
0.611 13.0 0.58 0.846
0.611 7.8 0.61 1.000
0.611 7.9 0.68 0.831
0.692 12.8 0.83 1.920
0.692 12.8 0.74 1.689
0.692 7.8 0.88 1.773
0.692 7.7 0.72 1.400
0.611 12.8 0.71 1.457
0.611 12.8 0.56 1.183
0.611 7.8 0.71 1.265
0.611 7.8 0.59 1.098
0.607 2.8 0.74 0.807
0.607 5.9 0.67 1.079
0.617 2.9 0.74 0.964
0.617 5.8 1.04 0.873
0.610 2.6 0.54 0.645
0.610 5.9 0.56 0.932Another approach is represented by empirical correlations,
which focus on the applicability of the method. Most often
empirical correlations are developed with the Buckingham-Pi-
Theorem (dimensional analysis). Thereby all variables which
are considered to have an influence on themass flow rate and
are independent from each other are combined in dimen-
sionless groups. These groups are fitted by means of an
appropriate equation form (mostly power-law) to measure-
ment data. Another method to develop empirical correlations
came up in the last years applying neural networks to find an
adequate equation form to fit the empirical parameters to
experimental results.
Shao et al. (2013) reviewed 20 empirical correlations for the
prediction of the mass flow rate through adiabatic capillary
tubes and compared the agreement of eleven representative
correlations with 182 experimental data points of different
sources, comprising five different refrigerants. Only data
which was not used for the development of the investigated
correlation was chosen for the comparison. Thus, due to the
lack of independent experimental data for R600a, the authors
could not check the validity of the correlations for this
refrigerant.
The recommendation of the review from Shao et al.
resulted in the correlation from Yang and Zhang (2009). This
correlation was developed with a neural network approach
and represents an expansion of an earlier work (Zhang and
Zhao, 2007) in order to also cover super critical flow of CO2.
The authors used 710 experimental data points with capillary
tube flow, including the results for R600a of Melo et al., to train
the neural network, i.e. to find an adequate equation form. In
within an error band of 15% is reported.
able, the capillary constantF, (Hermes et al., 2010). A fit on 761
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Measured mass flow rate / (kg h )-1
+10%
-10%
Melo et al. (1999)This work
Pred
icte
d m
ass
fl ow
rat
e /(k
g h-1
)
i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 8 ( 2 0 1 4 ) 2 7 5e2 8 0 279As Fig. 3 shows the empirical correlation from Yang and
Zhang predicts both the experimental results of Melo et al. as
well as our own points on R600a systematically by about 20%
too high.
3.3. Algebraic equationsthe paper a prediction of all 710 training data points of 93%
Fig. 3 e Prediction of the experimental data through the
correlation of Yang and Zhang (2009).Several scientists tried to develop an analytical description of
the capillary tube flow by introducing simplifying
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Pred
icte
d m
ass
flow
rat
e /(k
g h- 1
)
Measured mass flow rate / (kg h-1)
-10%
Melo et al. (1999)This work +10%
Fig. 4 e Prediction of the experimental data by Hermes
equation (Hermes et al., 2010).in-house data points with R134a and R600a resulted in a value
F 6.
_M FD5
L
"pin pf
vf pf pout
a ba2
ln
a pout ba pf b
!#vuut (1)
The parameters a and b, which represent fitting parameters
for the description of the specific volume in the two phase
domain, were adopted fromZhang andDing (2004) and Yilmaz
and Unal (1996) accordingly, where a vf 1 k, b vfpf k andk 1:63,105p0:72f . It is worth mentioning that the parameter kshould be dimensionless, but is not. In order to arrive at cor-
rect results Pascal as the physical unit of the pressure has to
be implemented.
The authors report an agreement of Equation (1) with their
experimental results of 89%within the aimed10% error band(Hermes et al., 2010). In case of R600a the database comprised
189 data points obtained from two different tube lengths with
one single inner diameter. The mass flow rate varied between
2 kg h1 and 4 kg h1 (about 150 We300 W refrigerationcapacity).
In Fig. 4 the experimental results of this work and the
published data of Melo et al. (1999) is compared with the re-
sults of the Hermes equation. As can be seen, the equation
also predicts the mass flow rates in the range from 0.65 kg h1
to 2 kg h1 covered in this work verywell. Out of the Design ofExperiments e scheme only one point lies outside the 10%
error bands. In total a prediction of 94% of both datasets
within an 10% error band is achieved.
4. Conclusions
The presented experimental results extend the published
database for R600amass flow rates through adiabatic capillary
tubes in the range of flow rates from 0.65 kg h1 to 2.0 kg h1. Atest rig was constructed which allows to measure the mass
flow rates through different capillary tubes under controlled
boundary conditions. By means of the statistical method
Factorial Design the complete range of small scale refrigera-
tion systems was covered with 16 tests. Additionally the re-
sults of sixmore tests, with lower subcooling of the refrigerant
at the capillary inlet and three additional capillary tubes, areassumptions for the calculation of the fluid properties along
the capillary tube. In this way they were able to transform the
governing differential equations into their integral form. They
obtained an algebraic equation which can predict the mass
flow rate or alternatively the geometry of the capillary tube for
given boundary conditions. Although empirical parameters
are included in these equations, too, they are based on a
physical background.
One of the first successful attempts on this field was the
one by Yilmaz and Unal (1996). This work was continued by
Zhang and Ding (2001, 2004) and Yang and Wang (2008). In
2010 Hermes et al. published an algebraic Equation (1) in
which all the empirical parameters are merged in one vari-reported. The comparison of existing correlations for adia-
batic capillary tubes and the experimental data produced a
good level of agreement with the semi-algebraic equation of
Hermes et al. from 2010.
Acknowledgments
We thank the students Adriano Ronzoni and Bruno Yuji
Kimura de Carvalho for their great help with the experimental
work within their project work at ITTK.
r e f e r e n c e s
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Experimental investigation of the refrigerant flow of isobutane (R600a) through adiabatic capillary tubes1 Introduction2 Experimental work2.1 Experimental setup2.2 Design of experiments2.3 Choked flow2.4 Experimental results
3 Comparison with available correlations3.1 Finite-volume based methods3.2 Empirical correlations3.3 Algebraic equations
4 ConclusionsAcknowledgmentsReferences